LMFDB - Embedded newform 728.2.c.a.365.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [728,2,Mod(365,728)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(728, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1, 0, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("728.365"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 728 = 2^{3} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	728.c (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [34] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.81310926715$
Analytic rank:	$0$
Dimension:	$34$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			365.4
Character	$\chi$	$=$	728.365
Dual form			728.2.c.a.365.3

$q$-expansion

comment:q-expansion

sage:f.q_expansion() # note that sage often uses an isomorphic number field

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.23674 + 0.685911i) q^{2} -0.302261i q^{3} +(1.05905 - 1.69659i) q^{4} -1.42871i q^{5} +(0.207324 + 0.373818i) q^{6} -1.00000 q^{7} +(-0.146067 + 2.82465i) q^{8} +2.90864 q^{9} +(0.979968 + 1.76694i) q^{10} +2.11205i q^{11} +(-0.512811 - 0.320110i) q^{12} +1.00000i q^{13} +(1.23674 - 0.685911i) q^{14} -0.431843 q^{15} +(-1.75681 - 3.59355i) q^{16} +1.07522 q^{17} +(-3.59723 + 1.99507i) q^{18} +3.52230i q^{19} +(-2.42393 - 1.51308i) q^{20} +0.302261i q^{21} +(-1.44868 - 2.61206i) q^{22} +5.47592 q^{23} +(0.853781 + 0.0441503i) q^{24} +2.95878 q^{25} +(-0.685911 - 1.23674i) q^{26} -1.78595i q^{27} +(-1.05905 + 1.69659i) q^{28} -3.52776i q^{29} +(0.534078 - 0.296206i) q^{30} -3.26031 q^{31} +(4.63758 + 3.23927i) q^{32} +0.638391 q^{33} +(-1.32977 + 0.737506i) q^{34} +1.42871i q^{35} +(3.08040 - 4.93476i) q^{36} -10.7444i q^{37} +(-2.41598 - 4.35617i) q^{38} +0.302261 q^{39} +(4.03561 + 0.208688i) q^{40} +9.67803 q^{41} +(-0.207324 - 0.373818i) q^{42} -9.02912i q^{43} +(3.58328 + 2.23678i) q^{44} -4.15560i q^{45} +(-6.77229 + 3.75599i) q^{46} +4.79483 q^{47} +(-1.08619 + 0.531015i) q^{48} +1.00000 q^{49} +(-3.65925 + 2.02946i) q^{50} -0.324997i q^{51} +(1.69659 + 1.05905i) q^{52} +0.906733i q^{53} +(1.22500 + 2.20875i) q^{54} +3.01752 q^{55} +(0.146067 - 2.82465i) q^{56} +1.06465 q^{57} +(2.41973 + 4.36293i) q^{58} +6.88024i q^{59} +(-0.457345 + 0.732659i) q^{60} +5.18552i q^{61} +(4.03216 - 2.23628i) q^{62} -2.90864 q^{63} +(-7.95733 - 0.825177i) q^{64} +1.42871 q^{65} +(-0.789524 + 0.437879i) q^{66} -5.46202i q^{67} +(1.13872 - 1.82421i) q^{68} -1.65516i q^{69} +(-0.979968 - 1.76694i) q^{70} +0.895683 q^{71} +(-0.424856 + 8.21589i) q^{72} -14.4466 q^{73} +(7.36973 + 13.2881i) q^{74} -0.894324i q^{75} +(5.97589 + 3.73030i) q^{76} -2.11205i q^{77} +(-0.373818 + 0.207324i) q^{78} +15.5041 q^{79} +(-5.13415 + 2.50998i) q^{80} +8.18609 q^{81} +(-11.9692 + 6.63826i) q^{82} +9.02943i q^{83} +(0.512811 + 0.320110i) q^{84} -1.53618i q^{85} +(6.19317 + 11.1667i) q^{86} -1.06630 q^{87} +(-5.96582 - 0.308502i) q^{88} +17.4324 q^{89} +(2.85037 + 5.13940i) q^{90} -1.00000i q^{91} +(5.79929 - 9.29037i) q^{92} +0.985464i q^{93} +(-5.92996 + 3.28883i) q^{94} +5.03235 q^{95} +(0.979105 - 1.40176i) q^{96} +4.26779 q^{97} +(-1.23674 + 0.685911i) q^{98} +6.14320i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 34 q + 2 q^{2} - 2 q^{4} - 6 q^{6} - 34 q^{7} + 8 q^{8} - 26 q^{9} - 4 q^{12} - 2 q^{14} - 8 q^{15} - 6 q^{16} - 20 q^{17} + 14 q^{18} - 4 q^{20} - 10 q^{22} - 20 q^{23} + 10 q^{24} - 22 q^{25} + 2 q^{28}+ \cdots + 2 q^{98}+O(q^{100}) $ 34 * q + 2 * q^2 - 2 * q^4 - 6 * q^6 - 34 * q^7 + 8 * q^8 - 26 * q^9 - 4 * q^12 - 2 * q^14 - 8 * q^15 - 6 * q^16 - 20 * q^17 + 14 * q^18 - 4 * q^20 - 10 * q^22 - 20 * q^23 + 10 * q^24 - 22 * q^25 + 2 * q^28 - 60 * q^30 + 16 * q^31 + 12 * q^32 - 8 * q^33 + 28 * q^34 - 4 * q^36 - 28 * q^38 + 8 * q^39 + 64 * q^40 + 8 * q^41 + 6 * q^42 + 24 * q^44 + 16 * q^46 + 24 * q^48 + 34 * q^49 + 10 * q^50 - 4 * q^52 - 18 * q^54 - 32 * q^55 - 8 * q^56 + 8 * q^57 + 44 * q^58 - 24 * q^60 + 60 * q^62 + 26 * q^63 - 2 * q^64 - 20 * q^65 + 24 * q^66 + 12 * q^68 + 64 * q^71 - 92 * q^72 - 22 * q^74 + 4 * q^76 + 20 * q^79 - 56 * q^80 - 6 * q^81 - 20 * q^82 + 4 * q^84 - 12 * q^86 - 56 * q^87 - 34 * q^88 - 4 * q^90 - 54 * q^92 + 12 * q^94 + 42 * q^96 + 2 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/728\mathbb{Z}\right)^\times$.

$n$	$183$	$365$	$521$	$561$
$\chi(n)$	$1$	$-1$	$1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.23674	+	0.685911i	−0.874507	+	0.485012i
$2$	−1.23674	+	0.685911i	−0.874507	+	0.485012i
$3$		−	0.302261i		−	0.174510i	−0.996186	−	0.0872551i	$-0.972190\pi$
$3$		−	0.302261i		−	0.174510i	0.996186	−	0.0872551i	$-0.0278095\pi$
$4$	1.05905	−	1.69659i	0.529527	−	0.848293i
$5$		−	1.42871i		−	0.638939i	−0.947597	−	0.319470i	$-0.896495\pi$
$5$		−	1.42871i		−	0.638939i	0.947597	−	0.319470i	$-0.103505\pi$
$6$	0.207324	+	0.373818i	0.0846396	+	0.152611i
$7$	−1.00000			−0.377964
$7$	−1.00000			−0.377964
$8$	−0.146067	+	2.82465i	−0.0516425	+	0.998666i
$9$	2.90864			0.969546
$10$	0.979968	+	1.76694i	0.309893	+	0.558757i
$11$			2.11205i			0.636808i	0.947955	+	0.318404i	$0.103147\pi$
$11$			2.11205i			0.636808i	−0.947955	+	0.318404i	$0.896853\pi$
$12$	−0.512811	−	0.320110i	−0.148036	−	0.0924078i
$13$			1.00000i			0.277350i
$13$			1.00000i			0.277350i
$14$	1.23674	−	0.685911i	0.330533	−	0.183317i
$15$	−0.431843			−0.111501
$16$	−1.75681	−	3.59355i	−0.439203	−	0.898388i
$17$	1.07522			0.260780			0.130390	−	0.991463i	$-0.458377\pi$
$17$	1.07522			0.260780			0.130390	+	0.991463i	$0.458377\pi$
$18$	−3.59723	+	1.99507i	−0.847875	+	0.470242i
$19$			3.52230i			0.808071i	0.914743	+	0.404036i	$0.132393\pi$
$19$			3.52230i			0.808071i	−0.914743	+	0.404036i	$0.867607\pi$
$20$	−2.42393	−	1.51308i	−0.542008	−	0.338335i
$21$			0.302261i			0.0659587i
$22$	−1.44868	−	2.61206i	−0.308860	−	0.556894i
$23$	5.47592			1.14181			0.570904	−	0.821017i	$-0.306593\pi$
$23$	5.47592			1.14181			0.570904	+	0.821017i	$0.306593\pi$
$24$	0.853781	+	0.0441503i	0.174277	+	0.00901214i
$25$	2.95878			0.591757
$26$	−0.685911	−	1.23674i	−0.134518	−	0.242545i
$27$		−	1.78595i		−	0.343706i
$28$	−1.05905	+	1.69659i	−0.200142	+	0.320625i
$29$		−	3.52776i		−	0.655089i	−0.944836	−	0.327545i	$-0.893779\pi$
$29$		−	3.52776i		−	0.655089i	0.944836	−	0.327545i	$-0.106221\pi$
$30$	0.534078	−	0.296206i	0.0975088	−	0.0540795i
$31$	−3.26031			−0.585569			−0.292785	−	0.956178i	$-0.594582\pi$
$31$	−3.26031			−0.585569			−0.292785	+	0.956178i	$0.594582\pi$
$32$	4.63758	+	3.23927i	0.819815	+	0.572628i
$33$	0.638391			0.111130
$34$	−1.32977	+	0.737506i	−0.228054	+	0.126481i
$35$			1.42871i			0.241496i
$36$	3.08040	−	4.93476i	0.513401	−	0.822460i
$37$		−	10.7444i		−	1.76637i	−0.469020	−	0.883187i	$-0.655393\pi$
$37$		−	10.7444i		−	1.76637i	0.469020	−	0.883187i	$-0.344607\pi$
$38$	−2.41598	−	4.35617i	−0.391924	−	0.706664i
$39$	0.302261			0.0484004
$40$	4.03561	+	0.208688i	0.638087	+	0.0329964i
$41$	9.67803			1.51145			0.755727	−	0.654887i	$-0.227284\pi$
$41$	9.67803			1.51145			0.755727	+	0.654887i	$0.227284\pi$
$42$	−0.207324	−	0.373818i	−0.0319907	−	0.0576813i
$43$		−	9.02912i		−	1.37693i	−0.725271	−	0.688464i	$-0.758285\pi$
$43$		−	9.02912i		−	1.37693i	0.725271	−	0.688464i	$-0.241715\pi$
$44$	3.58328	+	2.23678i	0.540200	+	0.337207i
$45$		−	4.15560i		−	0.619481i
$46$	−6.77229	+	3.75599i	−0.998520	+	0.553791i
$47$	4.79483			0.699398			0.349699	−	0.936862i	$-0.386284\pi$
$47$	4.79483			0.699398			0.349699	+	0.936862i	$0.386284\pi$
$48$	−1.08619	+	0.531015i	−0.156778	+	0.0766454i
$49$	1.00000			0.142857
$50$	−3.65925	+	2.02946i	−0.517496	+	0.287009i
$51$		−	0.324997i		−	0.0455087i
$52$	1.69659	+	1.05905i	0.235274	+	0.146864i
$53$			0.906733i			0.124549i	0.998059	+	0.0622747i	$0.0198355\pi$
$53$			0.906733i			0.124549i	−0.998059	+	0.0622747i	$0.980165\pi$
$54$	1.22500	+	2.20875i	0.166702	+	0.300573i
$55$	3.01752			0.406882
$56$	0.146067	−	2.82465i	0.0195190	−	0.377460i
$57$	1.06465			0.141017
$58$	2.41973	+	4.36293i	0.317726	+	0.572880i
$59$			6.88024i			0.895731i	0.894101	+	0.447865i	$0.147816\pi$
$59$			6.88024i			0.895731i	−0.894101	+	0.447865i	$0.852184\pi$
$60$	−0.457345	+	0.732659i	−0.0590430	+	0.0945859i
$61$			5.18552i			0.663938i	0.943290	+	0.331969i	$0.107713\pi$
$61$			5.18552i			0.663938i	−0.943290	+	0.331969i	$0.892287\pi$
$62$	4.03216	−	2.23628i	0.512085	−	0.284008i
$63$	−2.90864			−0.366454
$64$	−7.95733	−	0.825177i	−0.994666	−	0.103147i
$65$	1.42871			0.177210
$66$	−0.789524	+	0.437879i	−0.0971837	+	0.0538992i
$67$		−	5.46202i		−	0.667292i	−0.942699	−	0.333646i	$-0.891721\pi$
$67$		−	5.46202i		−	0.667292i	0.942699	−	0.333646i	$-0.108279\pi$
$68$	1.13872	−	1.82421i	0.138090	−	0.221218i
$69$		−	1.65516i		−	0.199257i
$70$	−0.979968	−	1.76694i	−0.117129	−	0.211190i
$71$	0.895683			0.106298			0.0531490	−	0.998587i	$-0.483074\pi$
$71$	0.895683			0.106298			0.0531490	+	0.998587i	$0.483074\pi$
$72$	−0.424856	+	8.21589i	−0.0500698	+	0.968252i
$73$	−14.4466			−1.69085			−0.845425	−	0.534094i	$-0.820653\pi$
$73$	−14.4466			−1.69085			−0.845425	+	0.534094i	$0.820653\pi$
$74$	7.36973	+	13.2881i	0.856713	+	1.54471i
$75$		−	0.894324i		−	0.103268i
$76$	5.97589	+	3.73030i	0.685481	+	0.427895i
$77$		−	2.11205i		−	0.240691i
$78$	−0.373818	+	0.207324i	−0.0423265	+	0.0234748i
$79$	15.5041			1.74435			0.872175	−	0.489195i	$-0.162709\pi$
$79$	15.5041			1.74435			0.872175	+	0.489195i	$0.162709\pi$
$80$	−5.13415	+	2.50998i	−0.574015	+	0.280624i
$81$	8.18609			0.909566
$82$	−11.9692	+	6.63826i	−1.32178	+	0.733073i
$83$			9.02943i			0.991109i	0.868577	+	0.495555i	$0.165035\pi$
$83$			9.02943i			0.991109i	−0.868577	+	0.495555i	$0.834965\pi$
$84$	0.512811	+	0.320110i	0.0559523	+	0.0349269i
$85$		−	1.53618i		−	0.166622i
$86$	6.19317	+	11.1667i	0.667827	+	1.20413i
$87$	−1.06630			−0.114320
$88$	−5.96582	−	0.308502i	−0.635959	−	0.0328864i
$89$	17.4324			1.84783			0.923917	−	0.382592i	$-0.124968\pi$
$89$	17.4324			1.84783			0.923917	+	0.382592i	$0.124968\pi$
$90$	2.85037	+	5.13940i	0.300456	+	0.541741i
$91$		−	1.00000i		−	0.104828i
$92$	5.79929	−	9.29037i	0.604618	−	0.968589i
$93$			0.985464i			0.102188i
$94$	−5.92996	+	3.28883i	−0.611629	+	0.339216i
$95$	5.03235			0.516308
$96$	0.979105	−	1.40176i	0.0999294	−	0.143066i
$97$	4.26779			0.433328			0.216664	−	0.976246i	$-0.430482\pi$
$97$	4.26779			0.433328			0.216664	+	0.976246i	$0.430482\pi$
$98$	−1.23674	+	0.685911i	−0.124930	+	0.0692874i
$99$			6.14320i			0.617415i
$100$	3.13351	−	5.01983i	0.313351	−	0.501983i
$101$		−	7.48731i		−	0.745015i	−0.928029	−	0.372508i	$-0.878498\pi$
$101$		−	7.48731i		−	0.745015i	0.928029	−	0.372508i	$-0.121502\pi$
$102$	0.222919	+	0.401937i	0.0220723	+	0.0397977i
$103$	−2.54505			−0.250771			−0.125386	−	0.992108i	$-0.540017\pi$
$103$	−2.54505			−0.250771			−0.125386	+	0.992108i	$0.540017\pi$
$104$	−2.82465	−	0.146067i	−0.276980	−	0.0143230i
$105$	0.431843			0.0421436
$106$	−0.621938	−	1.12139i	−0.0604080	−	0.108919i
$107$			6.43975i			0.622554i	0.950319	+	0.311277i	$0.100757\pi$
$107$			6.43975i			0.622554i	−0.950319	+	0.311277i	$0.899243\pi$
$108$	−3.03002	−	1.89141i	−0.291563	−	0.182001i
$109$		−	4.08818i		−	0.391577i	−0.980646	−	0.195788i	$-0.937273\pi$
$109$		−	4.08818i		−	0.391577i	0.980646	−	0.195788i	$-0.0627266\pi$
$110$	−3.73188	+	2.06975i	−0.355821	+	0.197343i
$111$	−3.24762			−0.308251
$112$	1.75681	+	3.59355i	0.166003	+	0.339559i
$113$	−10.4398			−0.982095			−0.491048	−	0.871133i	$-0.663386\pi$
$113$	−10.4398			−0.982095			−0.491048	+	0.871133i	$0.663386\pi$
$114$	−1.31670	+	0.730257i	−0.123320	+	0.0683948i
$115$		−	7.82351i		−	0.729546i
$116$	−5.98516	−	3.73609i	−0.555708	−	0.346887i
$117$			2.90864i			0.268904i
$118$	−4.71923	−	8.50907i	−0.434440	−	0.783323i
$119$	−1.07522			−0.0985655
$120$	0.0630780	−	1.21981i	0.00575821	−	0.111353i
$121$	6.53923			0.594475
$122$	−3.55681	−	6.41315i	−0.322018	−	0.580619i
$123$		−	2.92529i		−	0.263764i
$124$	−3.45284	+	5.53140i	−0.310075	+	0.496735i
$125$		−	11.3708i		−	1.01704i
$126$	3.59723	−	1.99507i	0.320467	−	0.177735i
$127$	−14.5900			−1.29466			−0.647328	−	0.762212i	$-0.724114\pi$
$127$	−14.5900			−1.29466			−0.647328	+	0.762212i	$0.724114\pi$
$128$	10.4071	−	4.43749i	0.919871	−	0.392222i
$129$	−2.72915			−0.240288
$130$	−1.76694	+	0.979968i	−0.154971	+	0.0859489i
$131$			8.54709i			0.746763i	0.927678	+	0.373381i	$0.121802\pi$
$131$			8.54709i			0.746763i	−0.927678	+	0.373381i	$0.878198\pi$
$132$	0.676090	−	1.08309i	0.0588461	−	0.0942705i
$133$		−	3.52230i		−	0.305422i
$134$	3.74646	+	6.75510i	0.323644	+	0.583551i
$135$	−2.55161			−0.219607
$136$	−0.157055	+	3.03713i	−0.0134673	+	0.260432i
$137$	−4.83312			−0.412921			−0.206461	−	0.978455i	$-0.566195\pi$
$137$	−4.83312			−0.412921			−0.206461	+	0.978455i	$0.566195\pi$
$138$	1.13529	+	2.04700i	0.0966422	+	0.174252i
$139$			20.7091i			1.75652i	0.478180	+	0.878262i	$0.341297\pi$
$139$			20.7091i			1.75652i	−0.478180	+	0.878262i	$0.658703\pi$
$140$	2.42393	+	1.51308i	0.204860	+	0.127879i
$141$		−	1.44929i		−	0.122052i
$142$	−1.10773	+	0.614359i	−0.0929584	+	0.0515558i
$143$	−2.11205			−0.176619
$144$	−5.10993	−	10.4523i	−0.425828	−	0.871028i
$145$	−5.04016			−0.418562
$146$	17.8667	−	9.90910i	1.47866	−	0.820083i
$147$		−	0.302261i		−	0.0249300i
$148$	−18.2289	−	11.3789i	−1.49840	−	0.935343i
$149$			5.23881i			0.429180i	0.976704	+	0.214590i	$0.0688415\pi$
$149$			5.23881i			0.429180i	−0.976704	+	0.214590i	$0.931159\pi$
$150$	0.613426	+	1.10605i	0.0500860	+	0.0903083i
$151$	−17.9190			−1.45823			−0.729113	−	0.684393i	$-0.760067\pi$
$151$	−17.9190			−1.45823			−0.729113	+	0.684393i	$0.760067\pi$
$152$	−9.94928	−	0.514492i	−0.806993	−	0.0417308i
$153$	3.12743			0.252838
$154$	1.44868	+	2.61206i	0.116738	+	0.210486i
$155$			4.65805i			0.374143i
$156$	0.320110	−	0.512811i	0.0256293	−	0.0410578i
$157$		−	0.00849787i		−	0.000678204i	−1.00000		0.000339102i	$-0.999892\pi$
$157$		−	0.00849787i		−	0.000678204i	1.00000		0.000339102i	$-0.000107939\pi$
$158$	−19.1746	+	10.6344i	−1.52545	+	0.846030i
$159$	0.274070			0.0217351
$160$	4.62799	−	6.62576i	0.365874	−	0.523812i
$161$	−5.47592			−0.431563
$162$	−10.1241	+	5.61493i	−0.795422	+	0.441150i
$163$			2.16450i			0.169537i	0.996401	+	0.0847684i	$0.0270150\pi$
$163$			2.16450i			0.169537i	−0.996401	+	0.0847684i	$0.972985\pi$
$164$	10.2495	−	16.4196i	0.800355	−	1.28216i
$165$		−	0.912076i		−	0.0710050i
$166$	−6.19338	−	11.1671i	−0.480700	−	0.866732i
$167$	−3.67872			−0.284668			−0.142334	−	0.989819i	$-0.545461\pi$
$167$	−3.67872			−0.284668			−0.142334	+	0.989819i	$0.545461\pi$
$168$	−0.853781	−	0.0441503i	−0.0658707	−	0.00340627i
$169$	−1.00000			−0.0769231
$170$	1.05368	+	1.89986i	0.0808139	+	0.145712i
$171$			10.2451i			0.783462i
$172$	−15.3187	−	9.56232i	−1.16804	−	0.729120i
$173$		−	22.9325i		−	1.74353i	−0.489927	−	0.871763i	$-0.662977\pi$
$173$		−	22.9325i		−	1.74353i	0.489927	−	0.871763i	$-0.337023\pi$
$174$	1.31874	−	0.731389i	0.0999735	−	0.0554465i
$175$	−2.95878			−0.223663
$176$	7.58978	−	3.71048i	0.572101	−	0.279688i
$177$	2.07962			0.156314
$178$	−21.5594	+	11.9571i	−1.61595	+	0.896222i
$179$		−	22.2311i		−	1.66163i	−0.556546	−	0.830817i	$-0.687874\pi$
$179$		−	22.2311i		−	1.66163i	0.556546	−	0.830817i	$-0.312126\pi$
$180$	−7.05034	−	4.40101i	−0.525502	−	0.328032i
$181$		−	3.16747i		−	0.235437i	−0.993047	−	0.117718i	$-0.962442\pi$
$181$		−	3.16747i		−	0.235437i	0.993047	−	0.117718i	$-0.0375580\pi$
$182$	0.685911	+	1.23674i	0.0508431	+	0.0916733i
$183$	1.56738			0.115864
$184$	−0.799851	+	15.4676i	−0.0589658	+	1.14028i
$185$	−15.3507			−1.12861
$186$	−0.675940	−	1.21876i	−0.0495623	−	0.0893641i
$187$			2.27093i			0.166067i
$188$	5.07798	−	8.13485i	0.370350	−	0.593295i
$189$			1.78595i			0.129909i
$190$	−6.22371	+	3.45174i	−0.451515	+	0.250416i
$191$	3.10833			0.224911			0.112455	−	0.993657i	$-0.464128\pi$
$191$	3.10833			0.224911			0.112455	+	0.993657i	$0.464128\pi$
$192$	−0.249419	+	2.40519i	−0.0180002	+	0.173579i
$193$	−8.51520			−0.612938			−0.306469	−	0.951881i	$-0.599148\pi$
$193$	−8.51520			−0.612938			−0.306469	+	0.951881i	$0.599148\pi$
$194$	−5.27814	+	2.92732i	−0.378949	+	0.210169i
$195$		−	0.431843i		−	0.0309249i
$196$	1.05905	−	1.69659i	0.0756467	−	0.121185i
$197$			14.2869i			1.01790i	0.860797	+	0.508948i	$0.169966\pi$
$197$			14.2869i			1.01790i	−0.860797	+	0.508948i	$0.830034\pi$
$198$	−4.21369	−	7.59755i	−0.299454	−	0.539934i
$199$	−26.2298			−1.85938			−0.929689	−	0.368345i	$-0.879924\pi$
$199$	−26.2298			−1.85938			−0.929689	+	0.368345i	$0.879924\pi$
$200$	−0.432181	+	8.35754i	−0.0305598	+	0.590967i
$201$	−1.65095			−0.116449
$202$	5.13563	+	9.25986i	0.361341	+	0.651521i
$203$			3.52776i			0.247600i
$204$	−0.551386	−	0.344189i	−0.0386047	−	0.0240981i
$205$		−	13.8271i		−	0.965727i
$206$	3.14757	−	1.74568i	0.219301	−	0.121627i
$207$	15.9275			1.10704
$208$	3.59355	−	1.75681i	0.249168	−	0.121813i
$209$	−7.43929			−0.514586
$210$	−0.534078	+	0.296206i	−0.0368549	+	0.0204401i
$211$		−	5.07186i		−	0.349161i	−0.984643	−	0.174580i	$-0.944143\pi$
$211$		−	5.07186i		−	0.349161i	0.984643	−	0.174580i	$-0.0558569\pi$
$212$	1.53835	+	0.960279i	0.105654	+	0.0659522i
$213$		−	0.270730i		−	0.0185501i
$214$	−4.41709	−	7.96430i	−0.301946	−	0.544428i
$215$	−12.9000			−0.879773
$216$	5.04469	+	0.260868i	0.343247	+	0.0177498i
$217$	3.26031			0.221324
$218$	2.80413	+	5.05602i	0.189920	+	0.342437i
$219$			4.36665i			0.295071i
$220$	3.19571	−	5.11948i	0.215455	−	0.345155i
$221$			1.07522i			0.0723273i
$222$	4.01646	−	2.22758i	0.269567	−	0.149505i
$223$	−8.10346			−0.542648			−0.271324	−	0.962488i	$-0.587461\pi$
$223$	−8.10346			−0.542648			−0.271324	+	0.962488i	$0.587461\pi$
$224$	−4.63758	−	3.23927i	−0.309861	−	0.216433i
$225$	8.60603			0.573736
$226$	12.9113	−	7.16078i	0.858850	−	0.476328i
$227$			22.2426i			1.47629i	0.674641	+	0.738146i	$0.264298\pi$
$227$			22.2426i			1.47629i	−0.674641	+	0.738146i	$0.735702\pi$
$228$	1.12752	−	1.80628i	0.0746721	−	0.119624i
$229$			0.687851i			0.0454545i	0.999742	+	0.0227272i	$0.00723493\pi$
$229$			0.687851i			0.0454545i	−0.999742	+	0.0227272i	$0.992765\pi$
$230$	5.36623	+	9.67565i	0.353839	+	0.637994i
$231$	−0.638391			−0.0420030
$232$	9.96471	+	0.515290i	0.654215	+	0.0338304i
$233$	21.7686			1.42611			0.713054	−	0.701109i	$-0.247311\pi$
$233$	21.7686			1.42611			0.713054	+	0.701109i	$0.247311\pi$
$234$	−1.99507	−	3.59723i	−0.130422	−	0.235158i
$235$		−	6.85043i		−	0.446873i
$236$	11.6729	+	7.28654i	0.759842	+	0.474313i
$237$		−	4.68628i		−	0.304407i
$238$	1.32977	−	0.737506i	0.0861962	−	0.0478054i
$239$	−12.4111			−0.802810			−0.401405	−	0.915901i	$-0.631478\pi$
$239$	−12.4111			−0.802810			−0.401405	+	0.915901i	$0.631478\pi$
$240$	0.758667	+	1.55185i	0.0489718	+	0.100172i
$241$	9.86867			0.635697			0.317848	−	0.948142i	$-0.397040\pi$
$241$	9.86867			0.635697			0.317848	+	0.948142i	$0.397040\pi$
$242$	−8.08732	+	4.48532i	−0.519873	+	0.288328i
$243$		−	7.83218i		−	0.502435i
$244$	8.79769	+	5.49174i	0.563214	+	0.351573i
$245$		−	1.42871i		−	0.0912770i
$246$	2.00648	+	3.61782i	0.127929	+	0.230664i
$247$	−3.52230			−0.224119
$248$	0.476224	−	9.20925i	0.0302403	−	0.584788i
$249$	2.72924			0.172959
$250$	7.79936	+	14.0627i	0.493275	+	0.889405i
$251$			12.2813i			0.775187i	0.921830	+	0.387593i	$0.126694\pi$
$251$			12.2813i			0.775187i	−0.921830	+	0.387593i	$0.873306\pi$
$252$	−3.08040	+	4.93476i	−0.194047	+	0.310860i
$253$			11.5654i			0.727113i
$254$	18.0441	−	10.0075i	1.13219	−	0.627924i
$255$	−0.464327			−0.0290773
$256$	−9.82722	+	12.6264i	−0.614201	+	0.789149i
$257$	−8.06646			−0.503172			−0.251586	−	0.967835i	$-0.580952\pi$
$257$	−8.06646			−0.503172			−0.251586	+	0.967835i	$0.580952\pi$
$258$	3.37525	−	1.87195i	0.210134	−	0.116543i
$259$			10.7444i			0.667627i
$260$	1.51308	−	2.42393i	0.0938373	−	0.150326i
$261$		−	10.2610i		−	0.635139i
$262$	−5.86254	−	10.5705i	−0.362189	−	0.653050i
$263$	16.3897			1.01063			0.505316	−	0.862934i	$-0.331376\pi$
$263$	16.3897			1.01063			0.505316	+	0.862934i	$0.331376\pi$
$264$	−0.0932478	+	1.80323i	−0.00573901	+	0.110981i
$265$	1.29546			0.0795795
$266$	2.41598	+	4.35617i	0.148133	+	0.267094i
$267$		−	5.26914i		−	0.322466i
$268$	−9.26679	−	5.78457i	−0.566059	−	0.353349i
$269$			25.7500i			1.57001i	0.619491	+	0.785004i	$0.287339\pi$
$269$			25.7500i			1.57001i	−0.619491	+	0.785004i	$0.712661\pi$
$270$	3.15567	−	1.75017i	0.192048	−	0.106512i
$271$	3.70858			0.225280			0.112640	−	0.993636i	$-0.464069\pi$
$271$	3.70858			0.225280			0.112640	+	0.993636i	$0.464069\pi$
$272$	−1.88896	−	3.86387i	−0.114535	−	0.234281i
$273$	−0.302261			−0.0182936
$274$	5.97731	−	3.31509i	0.361103	−	0.200272i
$275$			6.24911i			0.376836i
$276$	−2.80811	−	1.75290i	−0.169029	−	0.105512i
$277$			3.54833i			0.213199i	0.994302	+	0.106599i	$0.0339962\pi$
$277$			3.54833i			0.213199i	−0.994302	+	0.106599i	$0.966004\pi$
$278$	−14.2046	−	25.6118i	−0.851935	−	1.53609i
$279$	−9.48307			−0.567737
$280$	−4.03561	−	0.208688i	−0.241174	−	0.0124715i
$281$	−0.0751627			−0.00448383			−0.00224192	−	0.999997i	$-0.500714\pi$
$281$	−0.0751627			−0.00448383			−0.00224192	+	0.999997i	$0.500714\pi$
$282$	0.994082	+	1.79239i	0.0591967	+	0.106735i
$283$		−	22.3137i		−	1.32641i	−0.748437	−	0.663205i	$-0.769196\pi$
$283$		−	22.3137i		−	1.32641i	0.748437	−	0.663205i	$-0.230804\pi$
$284$	0.948576	−	1.51960i	0.0562876	−	0.0901719i
$285$		−	1.52108i		−	0.0901011i
$286$	2.61206	−	1.44868i	0.154455	−	0.0856623i
$287$	−9.67803			−0.571276
$288$	13.4890	+	9.42187i	0.794849	+	0.555189i
$289$	−15.8439			−0.931994
$290$	6.23336	−	3.45710i	0.366036	−	0.203008i
$291$		−	1.28998i		−	0.0756202i
$292$	−15.2997	+	24.5100i	−0.895350	+	1.43434i
$293$			15.1800i			0.886825i	0.896318	+	0.443412i	$0.146232\pi$
$293$			15.1800i			0.886825i	−0.896318	+	0.443412i	$0.853768\pi$
$294$	0.207324	+	0.373818i	0.0120914	+	0.0218015i
$295$	9.82987			0.572317
$296$	30.3493	+	1.56941i	1.76402	+	0.0912200i
$297$	3.77202			0.218875
$298$	−3.59335	−	6.47904i	−0.208157	−	0.375321i
$299$			5.47592i			0.316681i
$300$	−1.51730	−	0.947136i	−0.0876012	−	0.0546830i
$301$			9.02912i			0.520430i
$302$	22.1611	−	12.2908i	1.27523	−	0.707257i
$303$	−2.26312			−0.130013
$304$	12.6576	−	6.18802i	0.725961	−	0.354907i
$305$	7.40862			0.424216
$306$	−3.86782	+	2.14514i	−0.221109	+	0.122629i
$307$		−	10.7178i		−	0.611699i	−0.952080	−	0.305850i	$-0.901060\pi$
$307$		−	10.7178i		−	0.611699i	0.952080	−	0.305850i	$-0.0989405\pi$
$308$	−3.58328	−	2.23678i	−0.204177	−	0.127452i
$309$			0.769269i			0.0437622i
$310$	−3.19500	−	5.76079i	−0.181464	−	0.327191i
$311$	17.1663			0.973413			0.486707	−	0.873565i	$-0.338198\pi$
$311$	17.1663			0.973413			0.486707	+	0.873565i	$0.338198\pi$
$312$	−0.0441503	+	0.853781i	−0.00249952	+	0.0483358i
$313$	−11.5995			−0.655645			−0.327823	−	0.944739i	$-0.606315\pi$
$313$	−11.5995			−0.655645			−0.327823	+	0.944739i	$0.606315\pi$
$314$	0.00582878	+	0.0105097i	0.000328937	+	0.000593094i
$315$			4.15560i			0.234142i
$316$	16.4197	−	26.3041i	0.923679	−	1.47972i
$317$		−	7.72578i		−	0.433923i	−0.976180	−	0.216962i	$-0.930385\pi$
$317$		−	7.72578i		−	0.433923i	0.976180	−	0.216962i	$-0.0696146\pi$
$318$	−0.338953	+	0.187987i	−0.0190075	+	0.0105418i
$319$	7.45083			0.417166
$320$	−1.17894	+	11.3687i	−0.0659048	+	0.635531i
$321$	1.94648			0.108642
$322$	6.77229	−	3.75599i	0.377405	−	0.209313i
$323$			3.78726i			0.210729i
$324$	8.66951	−	13.8884i	0.481639	−	0.771579i
$325$			2.95878i			0.164124i
$326$	−1.48465	−	2.67693i	−0.0822274	−	0.148261i
$327$	−1.23570			−0.0683342
$328$	−1.41364	+	27.3371i	−0.0780552	+	1.50944i
$329$	−4.79483			−0.264348
$330$	0.625603	+	1.12800i	0.0344383	+	0.0620944i
$331$			7.83452i			0.430624i	0.976545	+	0.215312i	$0.0690769\pi$
$331$			7.83452i			0.430624i	−0.976545	+	0.215312i	$0.930923\pi$
$332$	15.3192	+	9.56265i	0.840751	+	0.524819i
$333$		−	31.2517i		−	1.71258i
$334$	4.54963	−	2.52328i	0.248944	−	0.138068i
$335$	−7.80365			−0.426359
$336$	1.08619	−	0.531015i	0.0592565	−	0.0289693i
$337$	−6.71021			−0.365528			−0.182764	−	0.983157i	$-0.558504\pi$
$337$	−6.71021			−0.365528			−0.182764	+	0.983157i	$0.558504\pi$
$338$	1.23674	−	0.685911i	0.0672698	−	0.0373086i
$339$			3.15554i			0.171386i
$340$	−2.60627	−	1.62690i	−0.141345	−	0.0882310i
$341$		−	6.88596i		−	0.372896i
$342$	−7.02722	−	12.6705i	−0.379989	−	0.685144i
$343$	−1.00000			−0.0539949
$344$	25.5041	+	1.31886i	1.37509	+	0.0711080i
$345$	−2.36474			−0.127313
$346$	15.7297	+	28.3616i	0.845632	+	1.52473i
$347$			28.7053i			1.54098i	0.637450	+	0.770492i	$0.279989\pi$
$347$			28.7053i			1.54098i	−0.637450	+	0.770492i	$0.720011\pi$
$348$	−1.12927	+	1.80908i	−0.0605354	+	0.0969767i
$349$			31.5592i			1.68933i	0.535298	+	0.844663i	$0.320199\pi$
$349$			31.5592i			1.68933i	−0.535298	+	0.844663i	$0.679801\pi$
$350$	3.65925	−	2.02946i	0.195595	−	0.108479i
$351$	1.78595			0.0953269
$352$	−6.84152	+	9.79481i	−0.364654	+	0.522065i
$353$	−32.1482			−1.71108			−0.855538	−	0.517741i	$-0.826773\pi$
$353$	−32.1482			−1.71108			−0.855538	+	0.517741i	$0.826773\pi$
$354$	−2.57196	+	1.42644i	−0.136698	+	0.0758142i
$355$		−	1.27967i		−	0.0679180i
$356$	18.4619	−	29.5756i	0.978478	−	1.56751i
$357$			0.324997i			0.0172007i
$358$	15.2486	+	27.4941i	0.805912	+	1.45311i
$359$	−0.201990			−0.0106606			−0.00533032	−	0.999986i	$-0.501697\pi$
$359$	−0.201990			−0.0106606			−0.00533032	+	0.999986i	$0.501697\pi$
$360$	11.7381	+	0.606997i	0.618654	+	0.0319915i
$361$	6.59340			0.347021
$362$	2.17260	+	3.91734i	0.114190	+	0.205891i
$363$		−	1.97655i		−	0.103742i
$364$	−1.69659	−	1.05905i	−0.0889253	−	0.0555095i
$365$			20.6401i			1.08035i
$366$	−1.93844	+	1.07508i	−0.101324	+	0.0561954i
$367$	12.2350			0.638659			0.319330	−	0.947644i	$-0.396542\pi$
$367$	12.2350			0.638659			0.319330	+	0.947644i	$0.396542\pi$
$368$	−9.62017	−	19.6780i	−0.501486	−	1.02579i
$369$	28.1499			1.46542
$370$	18.9848	−	10.5292i	0.986974	−	0.547388i
$371$		−	0.906733i		−	0.0470753i
$372$	1.67193	+	1.04366i	0.0866853	+	0.0541112i
$373$			30.5414i			1.58138i	0.612220	+	0.790688i	$0.290277\pi$
$373$			30.5414i			1.58138i	−0.612220	+	0.790688i	$0.709723\pi$
$374$	−1.55765	−	2.80855i	−0.0805444	−	0.145227i
$375$	−3.43695			−0.177483
$376$	−0.700367	+	13.5437i	−0.0361187	+	0.698465i
$377$	3.52776			0.181689
$378$	−1.22500	−	2.20875i	−0.0630073	−	0.113606i
$379$		−	23.3843i		−	1.20117i	−0.799560	−	0.600586i	$-0.794934\pi$
$379$		−	23.3843i		−	1.20117i	0.799560	−	0.600586i	$-0.205066\pi$
$380$	5.32953	−	8.53782i	0.273399	−	0.437981i
$381$			4.40999i			0.225931i
$382$	−3.84420	+	2.13204i	−0.196686	+	0.109084i
$383$	−25.5623			−1.30617			−0.653085	−	0.757285i	$-0.726526\pi$
$383$	−25.5623			−1.30617			−0.653085	+	0.757285i	$0.726526\pi$
$384$	−1.34128	−	3.14567i	−0.0684468	−	0.160527i
$385$	−3.01752			−0.153787
$386$	10.5311	−	5.84067i	0.536019	−	0.297282i
$387$		−	26.2624i		−	1.33500i
$388$	4.51981	−	7.24067i	0.229459	−	0.367589i
$389$			18.4359i			0.934735i	0.884063	+	0.467367i	$0.154797\pi$
$389$			18.4359i			0.934735i	−0.884063	+	0.467367i	$0.845203\pi$
$390$	0.296206	+	0.534078i	0.0149990	+	0.0270441i
$391$	5.88783			0.297760
$392$	−0.146067	+	2.82465i	−0.00737750	+	0.142667i
$393$	2.58345			0.130318
$394$	−9.79951	−	17.6691i	−0.493692	−	0.890158i
$395$		−	22.1509i		−	1.11453i
$396$	10.4225	+	6.50598i	0.523749	+	0.326938i
$397$		−	24.1909i		−	1.21411i	−0.794662	−	0.607053i	$-0.792352\pi$
$397$		−	24.1909i		−	1.21411i	0.794662	−	0.607053i	$-0.207648\pi$
$398$	32.4394	−	17.9913i	1.62604	−	0.901821i
$399$	−1.06465			−0.0532993
$400$	−5.19803	−	10.6325i	−0.259901	−	0.531627i
$401$	27.3572			1.36615			0.683076	−	0.730347i	$-0.260642\pi$
$401$	27.3572			1.36615			0.683076	+	0.730347i	$0.260642\pi$
$402$	2.04180	−	1.13241i	0.101836	−	0.0564793i
$403$		−	3.26031i		−	0.162408i
$404$	−12.7029	−	7.92946i	−0.631991	−	0.394505i
$405$		−	11.6956i		−	0.581157i
$406$	−2.41973	−	4.36293i	−0.120089	−	0.216528i
$407$	22.6928			1.12484
$408$	0.918005	+	0.0474714i	0.0454480	+	0.00235018i
$409$	−11.9361			−0.590204			−0.295102	−	0.955466i	$-0.595354\pi$
$409$	−11.9361			−0.590204			−0.295102	+	0.955466i	$0.595354\pi$
$410$	9.48416	+	17.1005i	0.468389	+	0.844535i
$411$			1.46086i			0.0720590i
$412$	−2.69534	+	4.31790i	−0.132790	+	0.212728i
$413$		−	6.88024i		−	0.338554i
$414$	−19.6982	+	10.9248i	−0.968111	+	0.536926i
$415$	12.9005			0.633258
$416$	−3.23927	+	4.63758i	−0.158818	+	0.227376i
$417$	6.25955			0.306531
$418$	9.20047	−	5.10269i	0.450010	−	0.249581i
$419$		−	2.55111i		−	0.124630i	−0.998057	−	0.0623150i	$-0.980152\pi$
$419$		−	2.55111i		−	0.124630i	0.998057	−	0.0623150i	$-0.0198484\pi$
$420$	0.457345	−	0.732659i	0.0223161	−	0.0357501i
$421$			37.9289i			1.84854i	0.381740	+	0.924270i	$0.375325\pi$
$421$			37.9289i			1.84854i	−0.381740	+	0.924270i	$0.624675\pi$
$422$	3.47884	+	6.27257i	0.169347	+	0.305344i
$423$	13.9464			0.678099
$424$	−2.56121	−	0.132444i	−0.124383	−	0.00643204i
$425$	3.18135			0.154318
$426$	0.185696	+	0.334822i	0.00899702	+	0.0162222i
$427$		−	5.18552i		−	0.250945i
$428$	10.9256	+	6.82004i	0.528109	+	0.329659i
$429$			0.638391i			0.0308218i
$430$	15.9540	−	8.84825i	0.769368	−	0.426701i
$431$	−3.23951			−0.156041			−0.0780207	−	0.996952i	$-0.524860\pi$
$431$	−3.23951			−0.156041			−0.0780207	+	0.996952i	$0.524860\pi$
$432$	−6.41790	+	3.13758i	−0.308781	+	0.150957i
$433$	−10.6772			−0.513114			−0.256557	−	0.966529i	$-0.582588\pi$
$433$	−10.6772			−0.513114			−0.256557	+	0.966529i	$0.582588\pi$
$434$	−4.03216	+	2.23628i	−0.193550	+	0.107345i
$435$			1.52344i			0.0730434i
$436$	−6.93596	−	4.32960i	−0.332172	−	0.207350i
$437$			19.2878i			0.922662i
$438$	−2.99513	−	5.40041i	−0.143113	−	0.258041i
$439$	−7.91420			−0.377724			−0.188862	−	0.982004i	$-0.560480\pi$
$439$	−7.91420			−0.377724			−0.188862	+	0.982004i	$0.560480\pi$
$440$	−0.440760	+	8.52344i	−0.0210124	+	0.406339i
$441$	2.90864			0.138507
$442$	−0.737506	−	1.32977i	−0.0350796	−	0.0632507i
$443$			0.488220i			0.0231960i	0.999933	+	0.0115980i	$0.00369185\pi$
$443$			0.488220i			0.0231960i	−0.999933	+	0.0115980i	$0.996308\pi$
$444$	−3.43940	+	5.50987i	−0.163227	+	0.261487i
$445$		−	24.9059i		−	1.18065i
$446$	10.0219	−	5.55825i	0.474550	−	0.263191i
$447$	1.58348			0.0748962
$448$	7.95733	+	0.825177i	0.375948	+	0.0389860i
$449$	−32.7761			−1.54680			−0.773399	−	0.633919i	$-0.781445\pi$
$449$	−32.7761			−1.54680			−0.773399	+	0.633919i	$0.781445\pi$
$450$	−10.6434	+	5.90297i	−0.501736	+	0.278269i
$451$			20.4405i			0.962506i
$452$	−11.0563	+	17.7120i	−0.520046	+	0.833105i
$453$			5.41620i			0.254475i
$454$	−15.2564	−	27.5083i	−0.716019	−	1.29103i
$455$	−1.42871			−0.0669790
$456$	−0.155511	+	3.00727i	−0.00728245	+	0.140829i
$457$	10.4564			0.489131			0.244566	−	0.969633i	$-0.421355\pi$
$457$	10.4564			0.489131			0.244566	+	0.969633i	$0.421355\pi$
$458$	−0.471804	−	0.850693i	−0.0220460	−	0.0397503i
$459$		−	1.92029i		−	0.0896315i
$460$	−13.2733	−	8.28551i	−0.618869	−	0.386314i
$461$		−	18.2242i		−	0.848786i	−0.905478	−	0.424393i	$-0.860487\pi$
$461$		−	18.2242i		−	0.848786i	0.905478	−	0.424393i	$-0.139513\pi$
$462$	0.789524	−	0.437879i	0.0367320	−	0.0203720i
$463$	12.6199			0.586498			0.293249	−	0.956036i	$-0.405264\pi$
$463$	12.6199			0.586498			0.293249	+	0.956036i	$0.405264\pi$
$464$	−12.6772	+	6.19762i	−0.588524	+	0.287717i
$465$	1.40794			0.0652918
$466$	−26.9221	+	14.9313i	−1.24714	+	0.691680i
$467$			4.87907i			0.225777i	0.993608	+	0.112888i	$0.0360102\pi$
$467$			4.87907i			0.225777i	−0.993608	+	0.112888i	$0.963990\pi$
$468$	4.93476	+	3.08040i	0.228109	+	0.142392i
$469$			5.46202i			0.252213i
$470$	4.69878	+	8.47220i	0.216739	+	0.390794i
$471$	−0.00256857			−0.000118353
$472$	−19.4343	−	1.00498i	−0.894535	−	0.0462578i
$473$	19.0700			0.876839
$474$	3.21437	+	5.79571i	0.147641	+	0.266206i
$475$			10.4217i			0.478182i
$476$	−1.13872	+	1.82421i	−0.0521930	+	0.0836124i
$477$			2.63736i			0.120756i
$478$	15.3494	−	8.51293i	0.702063	−	0.389373i
$479$	−18.0377			−0.824165			−0.412082	−	0.911147i	$-0.635198\pi$
$479$	−18.0377			−0.824165			−0.412082	+	0.911147i	$0.635198\pi$
$480$	−2.00271	−	1.39886i	−0.0914106	−	0.0638488i
$481$	10.7444			0.489904
$482$	−12.2050	+	6.76903i	−0.555922	+	0.308321i
$483$			1.65516i			0.0753122i
$484$	6.92539	−	11.0944i	0.314790	−	0.504289i
$485$		−	6.09743i		−	0.276870i
$486$	5.37218	+	9.68637i	0.243687	+	0.439383i
$487$	22.7622			1.03145			0.515726	−	0.856753i	$-0.327522\pi$
$487$	22.7622			1.03145			0.515726	+	0.856753i	$0.327522\pi$
$488$	−14.6473	−	0.757434i	−0.663052	−	0.0342874i
$489$	0.654243			0.0295859
$490$	0.979968	+	1.76694i	0.0442705	+	0.0798224i
$491$		−	22.4017i		−	1.01098i	−0.862833	−	0.505488i	$-0.831312\pi$
$491$		−	22.4017i		−	1.01098i	0.862833	−	0.505488i	$-0.168688\pi$
$492$	−4.96300	−	3.09803i	−0.223749	−	0.139670i
$493$		−	3.79313i		−	0.170834i
$494$	4.35617	−	2.41598i	0.195993	−	0.108700i
$495$	8.77686			0.394491
$496$	5.72776	+	11.7161i	0.257184	+	0.526068i
$497$	−0.895683			−0.0401769
$498$	−3.37536	+	1.87202i	−0.151254	+	0.0838870i
$499$			6.56942i			0.294088i	0.989130	+	0.147044i	$0.0469758\pi$
$499$			6.56942i			0.294088i	−0.989130	+	0.147044i	$0.953024\pi$
$500$	−19.2916	−	12.0423i	−0.862745	−	0.538547i
$501$			1.11193i			0.0496775i
$502$	−8.42385	−	15.1887i	−0.375975	−	0.677907i
$503$	−28.0909			−1.25251			−0.626256	−	0.779617i	$-0.715414\pi$
$503$	−28.0909			−1.25251			−0.626256	+	0.779617i	$0.715414\pi$
$504$	0.424856	−	8.21589i	0.0189246	−	0.365965i
$505$	−10.6972			−0.476019
$506$	−7.93286	−	14.3035i	−0.352659	−	0.635866i
$507$			0.302261i			0.0134239i
$508$	−15.4516	+	24.7532i	−0.685555	+	1.09825i
$509$		−	30.4909i		−	1.35149i	−0.737137	−	0.675744i	$-0.763823\pi$
$509$		−	30.4909i		−	1.35149i	0.737137	−	0.675744i	$-0.236177\pi$
$510$	0.574252	−	0.318487i	0.0254283	−	0.0141028i
$511$	14.4466			0.639081
$512$	3.49314	−	22.3562i	0.154377	−	0.988012i
$513$	6.29065			0.277739
$514$	9.97612	−	5.53287i	0.440028	−	0.244044i
$515$			3.63614i			0.160228i
$516$	−2.89031	+	4.63023i	−0.127239	+	0.203835i
$517$			10.1269i			0.445383i
$518$	−7.36973	−	13.2881i	−0.323807	−	0.583845i
$519$	−6.93160			−0.304263
$520$	−0.208688	+	4.03561i	−0.00915156	+	0.176973i
$521$	−45.5582			−1.99594			−0.997970	−	0.0636820i	$-0.979716\pi$
$521$	−45.5582			−1.99594			−0.997970	+	0.0636820i	$0.979716\pi$
$522$	7.03812	+	12.6902i	0.308050	+	0.555434i
$523$		−	6.33191i		−	0.276875i	−0.990371	−	0.138438i	$-0.955792\pi$
$523$		−	6.33191i		−	0.276875i	0.990371	−	0.138438i	$-0.0442080\pi$
$524$	14.5009	+	9.05182i	0.633474	+	0.395431i
$525$			0.894324i			0.0390315i
$526$	−20.2698	+	11.2419i	−0.883806	+	0.490169i
$527$	−3.50556			−0.152705
$528$	−1.12153	−	2.29409i	−0.0488085	−	0.0998375i
$529$	6.98571			0.303727
$530$	−1.60215	+	0.888570i	−0.0695929	+	0.0385970i
$531$			20.0121i			0.868452i
$532$	−5.97589	−	3.73030i	−0.259088	−	0.161729i
$533$			9.67803i			0.419202i
$534$	3.61416	+	6.51656i	0.156400	+	0.281999i
$535$	9.20055			0.397774
$536$	15.4283	+	0.797821i	0.666401	+	0.0344606i
$537$	−6.71960			−0.289972
$538$	−17.6622	−	31.8461i	−0.761473	−	1.37298i
$539$			2.11205i			0.0909726i
$540$	−2.70229	+	4.32902i	−0.116288	+	0.186291i
$541$		−	22.2376i		−	0.956068i	−0.878341	−	0.478034i	$-0.841350\pi$
$541$		−	22.2376i		−	0.956068i	0.878341	−	0.478034i	$-0.158650\pi$
$542$	−4.58655	+	2.54376i	−0.197009	+	0.109264i
$543$	−0.957403			−0.0410861
$544$	4.98642	+	3.48294i	0.213791	+	0.149330i
$545$	−5.84083			−0.250194
$546$	0.373818	−	0.207324i	0.0159979	−	0.00887264i
$547$		−	21.1582i		−	0.904658i	−0.891851	−	0.452329i	$-0.850593\pi$
$547$		−	21.1582i		−	0.904658i	0.891851	−	0.452329i	$-0.149407\pi$
$548$	−5.11853	+	8.19981i	−0.218653	+	0.350278i
$549$			15.0828i			0.643719i
$550$	−4.28633	−	7.72853i	−0.182770	−	0.329546i
$551$	12.4258			0.529359
$552$	4.67524	+	0.241764i	0.198991	+	0.0102901i
$553$	−15.5041			−0.659302
$554$	−2.43384	−	4.38836i	−0.103404	−	0.186444i
$555$			4.63991i			0.196953i
$556$	35.1348	+	21.9320i	1.49005	+	0.930126i
$557$		−	0.896820i		−	0.0379995i	−0.999819	−	0.0189997i	$-0.993952\pi$
$557$		−	0.896820i		−	0.0379995i	0.999819	−	0.0189997i	$-0.00604817\pi$
$558$	11.7281	−	6.50454i	0.496490	−	0.275359i
$559$	9.02912			0.381891
$560$	5.13415	−	2.50998i	0.216957	−	0.106066i
$561$	0.686412			0.0289803
$562$	0.0929568	−	0.0515549i	0.00392115	−	0.00217471i
$563$			5.18352i			0.218459i	0.994017	+	0.109230i	$0.0348384\pi$
$563$			5.18352i			0.218459i	−0.994017	+	0.109230i	$0.965162\pi$
$564$	−2.45884	−	1.53487i	−0.103536	−	0.0646298i
$565$			14.9155i			0.627499i
$566$	15.3052	+	27.5962i	0.643325	+	1.15996i
$567$	−8.18609			−0.343784
$568$	−0.130830	+	2.52999i	−0.00548950	+	0.106156i
$569$	−16.6719			−0.698924			−0.349462	−	0.936951i	$-0.613636\pi$
$569$	−16.6719			−0.698924			−0.349462	+	0.936951i	$0.613636\pi$
$570$	1.04333	+	1.88118i	0.0437001	+	0.0787941i
$571$		−	16.4548i		−	0.688611i	−0.938858	−	0.344306i	$-0.888114\pi$
$571$		−	16.4548i		−	0.688611i	0.938858	−	0.344306i	$-0.111886\pi$
$572$	−2.23678	+	3.58328i	−0.0935244	+	0.149825i
$573$		−	0.939526i		−	0.0392492i
$574$	11.9692	−	6.63826i	0.499585	−	0.277076i
$575$	16.2021			0.675673
$576$	−23.1450	−	2.40014i	−0.964375	−	0.100006i
$577$	0.0663045			0.00276029			0.00138015	−	0.999999i	$-0.499561\pi$
$577$	0.0663045			0.00276029			0.00138015	+	0.999999i	$0.499561\pi$
$578$	19.5948	−	10.8675i	0.815036	−	0.452028i
$579$			2.57381i			0.106964i
$580$	−5.33779	+	8.55106i	−0.221640	+	0.355063i
$581$		−	9.02943i		−	0.374604i
$582$	0.884813	+	1.59537i	0.0366767	+	0.0661304i
$583$	−1.91507			−0.0793141
$584$	2.11018	−	40.8067i	0.0873197	−	1.68859i
$585$	4.15560			0.171813
$586$	−10.4121	−	18.7737i	−0.430121	−	0.775535i
$587$		−	23.6255i		−	0.975127i	−0.873087	−	0.487564i	$-0.837886\pi$
$587$		−	23.6255i		−	0.975127i	0.873087	−	0.487564i	$-0.162114\pi$
$588$	−0.512811	−	0.320110i	−0.0211480	−	0.0132011i
$589$		−	11.4838i		−	0.473182i
$590$	−12.1570	+	6.74241i	−0.500496	+	0.277581i
$591$	4.31836			0.177633
$592$	−38.6107	+	18.8760i	−1.58689	+	0.775797i
$593$	−1.66405			−0.0683342			−0.0341671	−	0.999416i	$-0.510878\pi$
$593$	−1.66405			−0.0683342			−0.0341671	+	0.999416i	$0.510878\pi$
$594$	−4.66501	+	2.58727i	−0.191408	+	0.106157i
$595$			1.53618i			0.0629773i
$596$	8.88809	+	5.54817i	0.364070	+	0.227262i
$597$			7.92822i			0.324481i
$598$	−3.75599	−	6.77229i	−0.153594	−	0.276940i
$599$	−4.60064			−0.187977			−0.0939885	−	0.995573i	$-0.529962\pi$
$599$	−4.60064			−0.187977			−0.0939885	+	0.995573i	$0.529962\pi$
$600$	2.52615	+	0.130631i	0.103130	+	0.00533300i
$601$	−13.2087			−0.538794			−0.269397	−	0.963029i	$-0.586824\pi$
$601$	−13.2087			−0.538794			−0.269397	+	0.963029i	$0.586824\pi$
$602$	−6.19317	−	11.1667i	−0.252415	−	0.455120i
$603$		−	15.8870i		−	0.646970i
$604$	−18.9772	+	30.4011i	−0.772170	+	1.23700i
$605$		−	9.34267i		−	0.379833i
$606$	2.79889	−	1.55230i	0.113697	−	0.0630578i
$607$	12.3140			0.499811			0.249905	−	0.968270i	$-0.419601\pi$
$607$	12.3140			0.499811			0.249905	+	0.968270i	$0.419601\pi$
$608$	−11.4097	+	16.3349i	−0.462724	+	0.662469i
$609$	1.06630			0.0432088
$610$	−9.16253	+	5.08165i	−0.370980	+	0.205750i
$611$			4.79483i			0.193978i
$612$	3.31212	−	5.30596i	0.133884	−	0.214481i
$613$			35.6977i			1.44182i	0.693030	+	0.720909i	$0.256276\pi$
$613$			35.6977i			1.44182i	−0.693030	+	0.720909i	$0.743724\pi$
$614$	7.35148	+	13.2552i	0.296682	+	0.534936i
$615$	−4.17939			−0.168529
$616$	5.96582	+	0.308502i	0.240370	+	0.0124299i
$617$	−11.9160			−0.479720			−0.239860	−	0.970808i	$-0.577102\pi$
$617$	−11.9160			−0.479720			−0.239860	+	0.970808i	$0.577102\pi$
$618$	−0.527649	−	0.951385i	−0.0212252	−	0.0382703i
$619$		−	36.8286i		−	1.48027i	−0.672460	−	0.740134i	$-0.734762\pi$
$619$		−	36.8286i		−	1.48027i	0.672460	−	0.740134i	$-0.265238\pi$
$620$	7.90278	+	4.93312i	0.317383	+	0.198119i
$621$		−	9.77971i		−	0.392446i
$622$	−21.2303	+	11.7746i	−0.851257	+	0.472117i
$623$	−17.4324			−0.698416
$624$	−0.531015	−	1.08619i	−0.0212576	−	0.0434824i
$625$	−1.45168			−0.0580671
$626$	14.3456	−	7.95625i	0.573367	−	0.317996i
$627$			2.24860i			0.0898006i
$628$	−0.0144174	−	0.00899970i	−0.000575316	−	0.000359127i
$629$		−	11.5527i		−	0.460635i
$630$	−2.85037	−	5.13940i	−0.113562	−	0.204759i
$631$	37.1252			1.47793			0.738966	−	0.673743i	$-0.235314\pi$
$631$	37.1252			1.47793			0.738966	+	0.673743i	$0.235314\pi$
$632$	−2.26464	+	43.7937i	−0.0900825	+	1.74202i
$633$	−1.53302			−0.0609322
$634$	5.29920	+	9.55479i	0.210458	+	0.379469i
$635$			20.8449i			0.827206i
$636$	0.290254	−	0.464983i	0.0115093	−	0.0184378i
$637$			1.00000i			0.0396214i
$638$	−9.21474	+	5.11060i	−0.364815	+	0.202331i
$639$	2.60522			0.103061
$640$	−6.33989	−	14.8688i	−0.250606	−	0.587741i
$641$	6.56797			0.259419			0.129710	−	0.991552i	$-0.458595\pi$
$641$	6.56797			0.259419			0.129710	+	0.991552i	$0.458595\pi$
$642$	−2.40729	+	1.33511i	−0.0950083	+	0.0526927i
$643$			1.39342i			0.0549511i	0.999622	+	0.0274755i	$0.00874684\pi$
$643$			1.39342i			0.0549511i	−0.999622	+	0.0274755i	$0.991253\pi$
$644$	−5.79929	+	9.29037i	−0.228524	+	0.366092i
$645$			3.89916i			0.153529i
$646$	−2.59772	−	4.68385i	−0.102206	−	0.184284i
$647$	−35.5340			−1.39699			−0.698493	−	0.715617i	$-0.746146\pi$
$647$	−35.5340			−1.39699			−0.698493	+	0.715617i	$0.746146\pi$
$648$	−1.19572	+	23.1229i	−0.0469723	+	0.908352i
$649$	−14.5314			−0.570409
$650$	−2.02946	−	3.65925i	−0.0796020	−	0.143527i
$651$		−	0.985464i		−	0.0386234i
$652$	3.67226	+	2.29232i	0.143817	+	0.0897742i
$653$		−	13.3350i		−	0.521839i	−0.965361	−	0.260920i	$-0.915974\pi$
$653$		−	13.3350i		−	0.521839i	0.965361	−	0.260920i	$-0.0840258\pi$
$654$	1.52824	−	0.847577i	0.0597588	−	0.0331429i
$655$	12.2113			0.477136
$656$	−17.0025	−	34.7785i	−0.663835	−	1.35787i
$657$	−42.0200			−1.63936
$658$	5.92996	−	3.28883i	0.231174	−	0.128212i
$659$		−	32.7598i		−	1.27614i	−0.769978	−	0.638070i	$-0.779733\pi$
$659$		−	32.7598i		−	1.27614i	0.769978	−	0.638070i	$-0.220267\pi$
$660$	−1.54742	−	0.965937i	−0.0602331	−	0.0375991i
$661$			42.2267i			1.64243i	0.570620	+	0.821214i	$0.306703\pi$
$661$			42.2267i			1.64243i	−0.570620	+	0.821214i	$0.693297\pi$
$662$	−5.37378	−	9.68927i	−0.208858	−	0.376584i
$663$	0.324997			0.0126218
$664$	−25.5050	−	1.31890i	−0.989787	−	0.0511833i
$665$	−5.03235			−0.195146
$666$	21.4359	+	38.6502i	0.830623	+	1.49767i
$667$		−	19.3178i		−	0.747986i
$668$	−3.89596	+	6.24127i	−0.150739	+	0.241482i
$669$			2.44936i			0.0946976i
$670$	9.65108	−	5.35260i	0.372854	−	0.206789i
$671$	−10.9521			−0.422801
$672$	−0.979105	+	1.40176i	−0.0377698	+	0.0540739i
$673$	−9.96162			−0.383992			−0.191996	−	0.981396i	$-0.561496\pi$
$673$	−9.96162			−0.383992			−0.191996	+	0.981396i	$0.561496\pi$
$674$	8.29878	−	4.60260i	0.319657	−	0.177286i
$675$		−	5.28424i		−	0.203390i
$676$	−1.05905	+	1.69659i	−0.0407328	+	0.0652533i
$677$		−	5.80056i		−	0.222934i	−0.993768	−	0.111467i	$-0.964445\pi$
$677$		−	5.80056i		−	0.222934i	0.993768	−	0.111467i	$-0.0355549\pi$
$678$	−2.16442	−	3.90259i	−0.0831241	−	0.149878i
$679$	−4.26779			−0.163783
$680$	4.33918	+	0.224386i	0.166400	+	0.00860479i
$681$	6.72306			0.257628
$682$	4.72315	+	8.51614i	0.180859	+	0.326100i
$683$		−	11.3291i		−	0.433494i	−0.976228	−	0.216747i	$-0.930455\pi$
$683$		−	11.3291i		−	0.433494i	0.976228	−	0.216747i	$-0.0695447\pi$
$684$	17.3817	+	10.8501i	0.664606	+	0.414864i
$685$			6.90513i			0.263832i
$686$	1.23674	−	0.685911i	0.0472190	−	0.0261882i
$687$	0.207910			0.00793227
$688$	−32.4466	+	15.8625i	−1.23702	+	0.604751i
$689$	−0.906733			−0.0345438
$690$	2.92457	−	1.62200i	0.111336	−	0.0617485i
$691$		−	28.0266i		−	1.06618i	−0.846058	−	0.533092i	$-0.821030\pi$
$691$		−	28.0266i		−	1.06618i	0.846058	−	0.533092i	$-0.178970\pi$
$692$	−38.9070	−	24.2868i	−1.47902	−	0.923244i
$693$		−	6.14320i		−	0.233361i
$694$	−19.6893	−	35.5010i	−0.747395	−	1.34760i
$695$	29.5873			1.12231
$696$	0.155752	−	3.01194i	0.00590376	−	0.114167i
$697$	10.4060			0.394156
$698$	−21.6468	−	39.0306i	−0.819344	−	1.47733i
$699$		−	6.57979i		−	0.248871i
$700$	−3.13351	+	5.01983i	−0.118436	+	0.189732i
$701$			36.2401i			1.36877i	0.729121	+	0.684384i	$0.239929\pi$
$701$			36.2401i			1.36877i	−0.729121	+	0.684384i	$0.760071\pi$
$702$	−2.20875	+	1.22500i	−0.0833641	+	0.0462347i
$703$	37.8451			1.42736
$704$	1.74282	−	16.8063i	0.0656850	−	0.633412i
$705$	−2.07062			−0.0779839
$706$	39.7590	−	22.0508i	1.49635	−	0.829892i
$707$			7.48731i			0.281589i
$708$	2.20243	−	3.52826i	0.0827725	−	0.132600i
$709$		−	22.1194i		−	0.830710i	−0.909659	−	0.415355i	$-0.863657\pi$
$709$		−	22.1194i		−	0.830710i	0.909659	−	0.415355i	$-0.136343\pi$
$710$	0.877741	+	1.58262i	0.0329410	+	0.0593948i
$711$	45.0959			1.69123
$712$	−2.54630	+	49.2406i	−0.0954268	+	1.84537i
$713$	−17.8532			−0.668608
$714$	−0.222919	−	0.401937i	−0.00834254	−	0.0150421i
$715$			3.01752i			0.112849i
$716$	−37.7171	−	23.5440i	−1.40955	−	0.879879i
$717$			3.75140i			0.140099i
$718$	0.249810	−	0.138547i	0.00932281	−	0.00517054i
$719$	−19.9640			−0.744531			−0.372265	−	0.928126i	$-0.621419\pi$
$719$	−19.9640			−0.744531			−0.372265	+	0.928126i	$0.621419\pi$
$720$	−14.9334	+	7.30062i	−0.556534	+	0.272078i
$721$	2.54505			0.0947826
$722$	−8.15432	+	4.52248i	−0.303472	+	0.168309i
$723$		−	2.98291i		−	0.110936i
$724$	−5.37390	−	3.35452i	−0.199719	−	0.124670i
$725$		−	10.4379i		−	0.387653i
$726$	1.35574	+	2.44448i	0.0503161	+	0.0907231i
$727$	4.84254			0.179600			0.0897999	−	0.995960i	$-0.471377\pi$
$727$	4.84254			0.179600			0.0897999	+	0.995960i	$0.471377\pi$
$728$	2.82465	+	0.146067i	0.104689	+	0.00541360i
$729$	22.1909			0.821886
$730$	−14.1572	−	25.5264i	−0.523983	−	0.944774i
$731$		−	9.70831i		−	0.359075i
$732$	1.65994	−	2.65919i	0.0613531	−	0.0982867i
$733$		−	8.88437i		−	0.328152i	−0.986448	−	0.164076i	$-0.947536\pi$
$733$		−	8.88437i		−	0.328152i	0.986448	−	0.164076i	$-0.0524642\pi$
$734$	−15.1315	+	8.39209i	−0.558513	+	0.309758i
$735$	−0.431843			−0.0159288
$736$	25.3950	+	17.7380i	0.936072	+	0.653832i
$737$	11.5361			0.424937
$738$	−34.8141	+	19.3083i	−1.28152	+	0.710748i
$739$		−	10.4639i		−	0.384922i	−0.981305	−	0.192461i	$-0.938353\pi$
$739$		−	10.4639i		−	0.384922i	0.981305	−	0.192461i	$-0.0616469\pi$
$740$	−16.2572	+	26.0438i	−0.597627	+	0.957389i
$741$			1.06465i			0.0391110i
$742$	0.621938	+	1.12139i	0.0228321	+	0.0411677i
$743$	−39.6855			−1.45592			−0.727960	−	0.685620i	$-0.759531\pi$
$743$	−39.6855			−1.45592			−0.727960	+	0.685620i	$0.759531\pi$
$744$	−2.78359	−	0.143944i	−0.102052	−	0.00527724i
$745$	7.48474			0.274220
$746$	−20.9487	−	37.7718i	−0.766986	−	1.38292i
$747$			26.2634i			0.960926i
$748$	3.85283	+	2.40503i	0.140873	+	0.0879367i
$749$		−	6.43975i		−	0.235303i
$750$	4.25061	−	2.35744i	0.155210	−	0.0860815i
$751$	−33.4376			−1.22016			−0.610078	−	0.792342i	$-0.708862\pi$
$751$	−33.4376			−1.22016			−0.610078	+	0.792342i	$0.708862\pi$
$752$	−8.42362	−	17.2305i	−0.307178	−	0.628331i
$753$	3.71214			0.135278
$754$	−4.36293	+	2.41973i	−0.158888	+	0.0881214i
$755$			25.6011i			0.931718i
$756$	3.03002	+	1.89141i	0.110201	+	0.0687901i
$757$			45.0370i			1.63690i	0.574581	+	0.818448i	$0.305165\pi$
$757$			45.0370i			1.63690i	−0.574581	+	0.818448i	$0.694835\pi$
$758$	16.0396	+	28.9204i	0.582583	+	1.05043i
$759$	3.49578			0.126889
$760$	−0.735060	+	14.2146i	−0.0266634	+	0.515619i
$761$	13.7077			0.496905			0.248452	−	0.968644i	$-0.420078\pi$
$761$	13.7077			0.496905			0.248452	+	0.968644i	$0.420078\pi$
$762$	−3.02486	−	5.45401i	−0.109579	−	0.197578i
$763$			4.08818i			0.148002i
$764$	3.29189	−	5.27355i	0.119096	−	0.190790i
$765$		−	4.46820i		−	0.161548i
$766$	31.6139	−	17.5334i	1.14226	−	0.633508i
$767$	−6.88024			−0.248431
$768$	3.81646	+	2.97038i	0.137715	+	0.107184i
$769$	23.3751			0.842929			0.421464	−	0.906845i	$-0.361516\pi$
$769$	23.3751			0.842929			0.421464	+	0.906845i	$0.361516\pi$
$770$	3.73188	−	2.06975i	0.134488	−	0.0745885i
$771$			2.43817i			0.0878087i
$772$	−9.01805	+	14.4468i	−0.324567	+	0.519951i
$773$			23.7114i			0.852838i	0.904526	+	0.426419i	$0.140225\pi$
$773$			23.7114i			0.852838i	−0.904526	+	0.426419i	$0.859775\pi$
$774$	18.0137	+	32.4798i	0.647489	+	1.16746i
$775$	−9.64656			−0.346515
$776$	−0.623383	+	12.0550i	−0.0223781	+	0.432750i
$777$	3.24762			0.116508
$778$	−12.6453	−	22.8004i	−0.453358	−	0.817433i
$779$			34.0889i			1.22136i
$780$	−0.732659	−	0.457345i	−0.0262334	−	0.0163756i
$781$			1.89173i			0.0676915i
$782$	−7.28172	+	4.03853i	−0.260394	+	0.144417i
$783$	−6.30040			−0.225158
$784$	−1.75681	−	3.59355i	−0.0627433	−	0.128341i
$785$	−0.0121410			−0.000433331
$786$	−3.19506	+	1.77201i	−0.113964	+	0.0632057i
$787$		−	46.6267i		−	1.66206i	−0.556227	−	0.831030i	$-0.687751\pi$
$787$		−	46.6267i		−	1.66206i	0.556227	−	0.831030i	$-0.312249\pi$
$788$	24.2389	+	15.1305i	0.863475	+	0.539003i
$789$		−	4.95396i		−	0.176366i
$790$	15.1935	+	27.3949i	0.540562	+	0.974667i
$791$	10.4398			0.371197
$792$	−17.3524	−	0.897319i	−0.616591	−	0.0318849i
$793$	−5.18552			−0.184143
$794$	16.5928	+	29.9178i	0.588856	+	1.06174i
$795$		−	0.391567i		−	0.0138874i
$796$	−27.7787	+	44.5011i	−0.984590	+	1.57730i
$797$		−	25.0129i		−	0.886003i	−0.896521	−	0.443001i	$-0.853914\pi$
$797$		−	25.0129i		−	0.886003i	0.896521	−	0.443001i	$-0.146086\pi$
$798$	1.31670	−	0.730257i	0.0466106	−	0.0258508i
$799$	5.15551			0.182389
$800$	13.7216	+	9.58431i	0.485131	+	0.338857i
$801$	50.7047			1.79156
$802$	−33.8337	+	18.7646i	−1.19471	+	0.662601i
$803$		−	30.5121i		−	1.07675i
$804$	−1.74845	+	2.80098i	−0.0616630	+	0.0987831i
$805$			7.82351i			0.275743i
$806$	2.23628	+	4.03216i	0.0787697	+	0.142027i
$807$	7.78322			0.273982
$808$	21.1491	+	1.09365i	0.744021	+	0.0384744i
$809$	−6.23755			−0.219300			−0.109650	−	0.993970i	$-0.534973\pi$
$809$	−6.23755			−0.219300			−0.109650	+	0.993970i	$0.534973\pi$
$810$	8.02211	+	14.4644i	0.281868	+	0.508226i
$811$		−	30.5842i		−	1.07396i	−0.843596	−	0.536978i	$-0.819566\pi$
$811$		−	30.5842i		−	1.07396i	0.843596	−	0.536978i	$-0.180434\pi$
$812$	5.98516	+	3.73609i	0.210038	+	0.131111i
$813$		−	1.12096i		−	0.0393137i
$814$	−28.0652	+	15.5653i	−0.983683	+	0.545562i
$815$	3.09245			0.108324
$816$	−1.16789	+	0.570959i	−0.0408845	+	0.0199876i
$817$	31.8033			1.11266
$818$	14.7619	−	8.18712i	0.516138	−	0.286256i
$819$		−	2.90864i		−	0.101636i
$820$	−23.4589	−	14.6436i	−0.819220	−	0.511378i
$821$			31.2474i			1.09054i	0.838260	+	0.545271i	$0.183573\pi$
$821$			31.2474i			1.09054i	−0.838260	+	0.545271i	$0.816427\pi$
$822$	−1.00202	−	1.80671i	−0.0349495	−	0.0630161i
$823$	57.0364			1.98816			0.994082	−	0.108628i	$-0.0346458\pi$
$823$	57.0364			1.98816			0.994082	+	0.108628i	$0.0346458\pi$
$824$	0.371748	−	7.18889i	0.0129505	−	0.250437i
$825$	1.88886			0.0657617
$826$	4.71923	+	8.50907i	0.164203	+	0.296068i
$827$		−	22.0341i		−	0.766200i	−0.923707	−	0.383100i	$-0.874857\pi$
$827$		−	22.0341i		−	0.766200i	0.923707	−	0.383100i	$-0.125143\pi$
$828$	16.8680	−	27.0223i	0.586205	−	0.939091i
$829$		−	1.38481i		−	0.0480963i	−0.999711	−	0.0240482i	$-0.992344\pi$
$829$		−	1.38481i		−	0.0480963i	0.999711	−	0.0240482i	$-0.00765551\pi$
$830$	−15.9545	+	8.84856i	−0.553789	+	0.307138i
$831$	1.07252			0.0372053
$832$	0.825177	−	7.95733i	0.0286079	−	0.275871i
$833$	1.07522			0.0372542
$834$	−7.74143	+	4.29349i	−0.268064	+	0.148671i
$835$			5.25584i			0.181886i
$836$	−7.87860	+	12.6214i	−0.272487	+	0.436520i
$837$			5.82275i			0.201264i
$838$	1.74984	+	3.15507i	0.0604471	+	0.108990i
$839$	1.94568			0.0671723			0.0335861	−	0.999436i	$-0.489307\pi$
$839$	1.94568			0.0671723			0.0335861	+	0.999436i	$0.489307\pi$
$840$	−0.0630780	+	1.21981i	−0.00217640	+	0.0420873i
$841$	16.5549			0.570858
$842$	−26.0158	−	46.9081i	−0.896564	−	1.61656i
$843$			0.0227187i			0.000782475i
$844$	−8.60484	−	5.37136i	−0.296191	−	0.184890i
$845$			1.42871i			0.0491492i
$846$	−17.2481	+	9.56601i	−0.593002	+	0.328886i
$847$	−6.53923			−0.224690
$848$	3.25839	−	1.59296i	0.111894	−	0.0547025i
$849$	−6.74455			−0.231472
$850$	−3.93450	+	2.18212i	−0.134952	+	0.0748462i
$851$		−	58.8357i		−	2.01686i
$852$	−0.459316	−	0.286717i	−0.0157359	−	0.00982277i
$853$		−	3.26963i		−	0.111950i	−0.998432	−	0.0559749i	$-0.982173\pi$
$853$		−	3.26963i		−	0.111950i	0.998432	−	0.0559749i	$-0.0178267\pi$
$854$	3.55681	+	6.41315i	0.121711	+	0.219453i
$855$	14.6373			0.500585
$856$	−18.1901	−	0.940635i	−0.621724	−	0.0321503i
$857$	49.4615			1.68957			0.844786	−	0.535104i	$-0.179728\pi$
$857$	49.4615			1.68957			0.844786	+	0.535104i	$0.179728\pi$
$858$	−0.437879	−	0.789524i	−0.0149489	−	0.0269539i
$859$			39.4168i			1.34489i	0.740149	+	0.672443i	$0.234755\pi$
$859$			39.4168i			1.34489i	−0.740149	+	0.672443i	$0.765245\pi$
$860$	−13.6618	+	21.8860i	−0.465863	+	0.746306i
$861$			2.92529i			0.0996935i
$862$	4.00643	−	2.22201i	0.136459	−	0.0756820i
$863$	1.05337			0.0358572			0.0179286	−	0.999839i	$-0.494293\pi$
$863$	1.05337			0.0358572			0.0179286	+	0.999839i	$0.494293\pi$
$864$	5.78518	−	8.28247i	0.196816	−	0.281775i
$865$	−32.7639			−1.11401
$866$	13.2049	−	7.32361i	0.448722	−	0.248866i
$867$			4.78899i			0.162642i
$868$	3.45284	−	5.53140i	0.117197	−	0.187748i
$869$			32.7455i			1.11082i
$870$	−1.04494	−	1.88410i	−0.0354269	−	0.0638770i
$871$	5.46202			0.185073
$872$	11.5477	+	0.597149i	0.391054	+	0.0202220i
$873$	12.4134			0.420131
$874$	−13.2297	−	23.8540i	−0.447502	−	0.806875i
$875$			11.3708i			0.384403i
$876$	7.40839	+	4.62451i	0.250306	+	0.156248i
$877$			13.9600i			0.471394i	0.971827	+	0.235697i	$0.0757373\pi$
$877$			13.9600i			0.471394i	−0.971827	+	0.235697i	$0.924263\pi$
$878$	9.78781	−	5.42844i	0.330323	−	0.183201i
$879$	4.58831			0.154760
$880$	−5.30121	−	10.8436i	−0.178704	−	0.365538i
$881$	23.8927			0.804967			0.402483	−	0.915427i	$-0.368147\pi$
$881$	23.8927			0.804967			0.402483	+	0.915427i	$0.368147\pi$
$882$	−3.59723	+	1.99507i	−0.121125	+	0.0671774i
$883$			36.0747i			1.21401i	0.794698	+	0.607005i	$0.207629\pi$
$883$			36.0747i			1.21401i	−0.794698	+	0.607005i	$0.792371\pi$
$884$	1.82421	+	1.13872i	0.0613547	+	0.0382992i
$885$		−	2.97118i		−	0.0998752i
$886$	−0.334876	−	0.603802i	−0.0112504	−	0.0202851i
$887$	16.9060			0.567647			0.283824	−	0.958877i	$-0.408397\pi$
$887$	16.9060			0.567647			0.283824	+	0.958877i	$0.408397\pi$
$888$	0.474370	−	9.17340i	0.0159188	−	0.307839i
$889$	14.5900			0.489334
$890$	17.0832	+	30.8022i	0.572631	+	1.03249i
$891$			17.2895i			0.579219i
$892$	−8.58200	+	13.7482i	−0.287347	+	0.460325i
$893$			16.8888i			0.565163i
$894$	−1.95836	+	1.08613i	−0.0654973	+	0.0363256i
$895$	−31.7619			−1.06168
$896$	−10.4071	+	4.43749i	−0.347678	+	0.148246i
$897$	1.65516			0.0552640
$898$	40.5355	−	22.4815i	1.35269	−	0.750216i
$899$			11.5016i			0.383600i
$900$	9.11425	−	14.6009i	0.303808	−	0.486696i
$901$			0.974940i			0.0324800i
$902$	−14.0204	−	25.2796i	−0.466827	−	0.841719i
$903$	2.72915			0.0908203
$904$	1.52491	−	29.4889i	0.0507178	−	0.980785i
$905$	−4.52541			−0.150430
$906$	−3.71503	−	6.69844i	−0.123424	−	0.222541i
$907$		−	22.2018i		−	0.737200i	−0.929588	−	0.368600i	$-0.879837\pi$
$907$		−	22.2018i		−	0.737200i	0.929588	−	0.368600i	$-0.120163\pi$
$908$	37.7365	+	23.5561i	1.25233	+	0.781736i
$909$		−	21.7779i		−	0.722327i
$910$	1.76694	−	0.979968i	0.0585737	−	0.0324856i
$911$	43.7053			1.44802			0.724011	−	0.689788i	$-0.242296\pi$
$911$	43.7053			1.44802			0.724011	+	0.689788i	$0.242296\pi$
$912$	−1.87040	−	3.82588i	−0.0619350	−	0.126688i
$913$	−19.0707			−0.631147
$914$	−12.9319	+	7.17218i	−0.427749	+	0.237235i
$915$		−	2.23933i		−	0.0740300i
$916$	1.16700	+	0.728471i	0.0385587	+	0.0240694i
$917$		−	8.54709i		−	0.282250i
$918$	1.31715	+	2.37490i	0.0434724	+	0.0783834i
$919$	−44.9547			−1.48292			−0.741459	−	0.670998i	$-0.765866\pi$
$919$	−44.9547			−1.48292			−0.741459	+	0.670998i	$0.765866\pi$
$920$	22.0987	+	1.14276i	0.728573	+	0.0376756i
$921$	−3.23958			−0.106748
$922$	12.5002	+	22.5386i	0.411672	+	0.742270i
$923$			0.895683i			0.0294818i
$924$	−0.676090	+	1.08309i	−0.0222417	+	0.0356309i
$925$		−	31.7905i		−	1.04526i
$926$	−15.6076	+	8.65614i	−0.512897	+	0.284459i
$927$	−7.40263			−0.243134
$928$	11.4274	−	16.3603i	0.375122	−	0.537052i
$929$	11.1318			0.365222			0.182611	−	0.983185i	$-0.441545\pi$
$929$	11.1318			0.365222			0.182611	+	0.983185i	$0.441545\pi$
$930$	−1.74126	+	0.965724i	−0.0570982	+	0.0316673i
$931$			3.52230i			0.115439i
$932$	23.0541	−	36.9323i	0.755162	−	1.20976i
$933$		−	5.18871i		−	0.169871i
$934$	−3.34661	−	6.03415i	−0.109504	−	0.197443i
$935$	3.24450			0.106107
$936$	−8.21589	−	0.424856i	−0.268545	−	0.0138869i
$937$	20.9629			0.684827			0.342413	−	0.939549i	$-0.388756\pi$
$937$	20.9629			0.684827			0.342413	+	0.939549i	$0.388756\pi$
$938$	−3.74646	−	6.75510i	−0.122326	−	0.220562i
$939$			3.50609i			0.114417i
$940$	−11.6223	−	7.25497i	−0.379079	−	0.236631i
$941$			0.215532i			0.00702615i	0.999994	+	0.00351308i	$0.00111825\pi$
$941$			0.215532i			0.00702615i	−0.999994	+	0.00351308i	$0.998882\pi$
$942$	0.00317666	−	0.00176181i	0.000103501	−	5.74029e-5i
$943$	52.9961			1.72579
$944$	24.7245	−	12.0873i	0.804713	−	0.393408i
$945$	2.55161			0.0830037
$946$	−23.5846	+	13.0803i	−0.766802	+	0.425278i
$947$		−	53.2972i		−	1.73193i	−0.500108	−	0.865963i	$-0.666706\pi$
$947$		−	53.2972i		−	1.73193i	0.500108	−	0.865963i	$-0.333294\pi$
$948$	−7.95068	−	4.96302i	−0.258226	−	0.161191i
$949$		−	14.4466i		−	0.468957i
$950$	−7.14837	−	12.8890i	−0.231924	−	0.418173i
$951$	−2.33520			−0.0757240
$952$	0.157055	−	3.03713i	0.00509017	−	0.0984339i
$953$	−56.7114			−1.83706			−0.918531	−	0.395349i	$-0.870624\pi$
$953$	−56.7114			−1.83706			−0.918531	+	0.395349i	$0.870624\pi$
$954$	−1.80899	−	3.26173i	−0.0585683	−	0.105602i
$955$		−	4.44091i		−	0.143704i
$956$	−13.1441	+	21.0566i	−0.425109	+	0.681018i
$957$		−	2.25209i		−	0.0727998i
$958$	22.3080	−	12.3723i	0.720738	−	0.399730i
$959$	4.83312			0.156070
$960$	3.43632	+	0.356347i	0.110907	+	0.0115011i
$961$	−20.3704			−0.657108
$962$	−13.2881	+	7.36973i	−0.428425	+	0.237609i
$963$			18.7309i			0.603595i
$964$	10.4514	−	16.7431i	0.336618	−	0.539257i
$965$			12.1658i			0.391630i
$966$	−1.13529	−	2.04700i	−0.0365273	−	0.0658611i
$967$	23.7485			0.763699			0.381850	−	0.924224i	$-0.375287\pi$
$967$	23.7485			0.763699			0.381850	+	0.924224i	$0.375287\pi$
$968$	−0.955165	+	18.4710i	−0.0307002	+	0.593682i
$969$	1.14474			0.0367743
$970$	4.18229	+	7.54094i	0.134285	+	0.242125i
$971$		−	28.6064i		−	0.918022i	−0.888431	−	0.459011i	$-0.848204\pi$
$971$		−	28.6064i		−	0.918022i	0.888431	−	0.459011i	$-0.151796\pi$
$972$	−13.2880	−	8.29469i	−0.426212	−	0.266052i
$973$		−	20.7091i		−	0.663903i
$974$	−28.1509	+	15.6128i	−0.902013	+	0.500267i
$975$	0.894324			0.0286413
$976$	18.6344	−	9.10999i	0.596474	−	0.291604i
$977$	18.5455			0.593323			0.296661	−	0.954983i	$-0.404127\pi$
$977$	18.5455			0.593323			0.296661	+	0.954983i	$0.404127\pi$
$978$	−0.809129	+	0.448752i	−0.0258731	+	0.0143495i
$979$			36.8183i			1.17672i
$980$	−2.42393	−	1.51308i	−0.0774297	−	0.0483336i
$981$		−	11.8910i		−	0.379652i
$982$	15.3656	+	27.7051i	0.490336	+	0.884107i
$983$	−57.1876			−1.82400			−0.912001	−	0.410188i	$-0.865463\pi$
$983$	−57.1876			−1.82400			−0.912001	+	0.410188i	$0.865463\pi$
$984$	8.26292	+	0.427288i	0.263412	+	0.0136214i
$985$	20.4118			0.650374
$986$	2.60175	+	4.69112i	0.0828565	+	0.149396i
$987$			1.44929i			0.0461314i
$988$	−3.73030	+	5.97589i	−0.118677	+	0.190118i
$989$		−	49.4427i		−	1.57219i
$990$	−10.8547	+	6.02014i	−0.344985	+	0.191333i
$991$	−0.0362040			−0.00115006			−0.000575029	−	1.00000i	$-0.500183\pi$
$991$	−0.0362040			−0.00115006			−0.000575029		1.00000i	$0.500183\pi$
$992$	−15.1199	−	10.5610i	−0.480059	−	0.335313i
$993$	2.36807			0.0751484
$994$	1.10773	−	0.614359i	0.0351350	−	0.0194863i
$995$			37.4748i			1.18803i
$996$	2.89041	−	4.63040i	0.0915862	−	0.146720i
$997$			22.5909i			0.715462i	0.933825	+	0.357731i	$0.116450\pi$
$997$			22.5909i			0.715462i	−0.933825	+	0.357731i	$0.883550\pi$
$998$	−4.50604	−	8.12467i	−0.142636	−	0.257182i
$999$	−19.1890			−0.607114

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	728.2.c.a.365.4	yes	34
4.3	odd	2		2912.2.c.a.1457.20		34
8.3	odd	2		2912.2.c.a.1457.15		34
8.5	even	2	inner	728.2.c.a.365.3	✓	34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
728.2.c.a.365.3	✓	34	8.5	even	2	inner
728.2.c.a.365.4	yes	34	1.1	even	1	trivial
2912.2.c.a.1457.15		34	8.3	odd	2
2912.2.c.a.1457.20		34	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 728 = 2^{3} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	728.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.23674 + 0.685911i) q^{2} -0.302261i q^{3} +(1.05905 - 1.69659i) q^{4} -1.42871i q^{5} +(0.207324 + 0.373818i) q^{6} -1.00000 q^{7} +(-0.146067 + 2.82465i) q^{8} +2.90864 q^{9} +(0.979968 + 1.76694i) q^{10} +2.11205i q^{11} +(-0.512811 - 0.320110i) q^{12} +1.00000i q^{13} +(1.23674 - 0.685911i) q^{14} -0.431843 q^{15} +(-1.75681 - 3.59355i) q^{16} +1.07522 q^{17} +(-3.59723 + 1.99507i) q^{18} +3.52230i q^{19} +(-2.42393 - 1.51308i) q^{20} +0.302261i q^{21} +(-1.44868 - 2.61206i) q^{22} +5.47592 q^{23} +(0.853781 + 0.0441503i) q^{24} +2.95878 q^{25} +(-0.685911 - 1.23674i) q^{26} -1.78595i q^{27} +(-1.05905 + 1.69659i) q^{28} -3.52776i q^{29} +(0.534078 - 0.296206i) q^{30} -3.26031 q^{31} +(4.63758 + 3.23927i) q^{32} +0.638391 q^{33} +(-1.32977 + 0.737506i) q^{34} +1.42871i q^{35} +(3.08040 - 4.93476i) q^{36} -10.7444i q^{37} +(-2.41598 - 4.35617i) q^{38} +0.302261 q^{39} +(4.03561 + 0.208688i) q^{40} +9.67803 q^{41} +(-0.207324 - 0.373818i) q^{42} -9.02912i q^{43} +(3.58328 + 2.23678i) q^{44} -4.15560i q^{45} +(-6.77229 + 3.75599i) q^{46} +4.79483 q^{47} +(-1.08619 + 0.531015i) q^{48} +1.00000 q^{49} +(-3.65925 + 2.02946i) q^{50} -0.324997i q^{51} +(1.69659 + 1.05905i) q^{52} +0.906733i q^{53} +(1.22500 + 2.20875i) q^{54} +3.01752 q^{55} +(0.146067 - 2.82465i) q^{56} +1.06465 q^{57} +(2.41973 + 4.36293i) q^{58} +6.88024i q^{59} +(-0.457345 + 0.732659i) q^{60} +5.18552i q^{61} +(4.03216 - 2.23628i) q^{62} -2.90864 q^{63} +(-7.95733 - 0.825177i) q^{64} +1.42871 q^{65} +(-0.789524 + 0.437879i) q^{66} -5.46202i q^{67} +(1.13872 - 1.82421i) q^{68} -1.65516i q^{69} +(-0.979968 - 1.76694i) q^{70} +0.895683 q^{71} +(-0.424856 + 8.21589i) q^{72} -14.4466 q^{73} +(7.36973 + 13.2881i) q^{74} -0.894324i q^{75} +(5.97589 + 3.73030i) q^{76} -2.11205i q^{77} +(-0.373818 + 0.207324i) q^{78} +15.5041 q^{79} +(-5.13415 + 2.50998i) q^{80} +8.18609 q^{81} +(-11.9692 + 6.63826i) q^{82} +9.02943i q^{83} +(0.512811 + 0.320110i) q^{84} -1.53618i q^{85} +(6.19317 + 11.1667i) q^{86} -1.06630 q^{87} +(-5.96582 - 0.308502i) q^{88} +17.4324 q^{89} +(2.85037 + 5.13940i) q^{90} -1.00000i q^{91} +(5.79929 - 9.29037i) q^{92} +0.985464i q^{93} +(-5.92996 + 3.28883i) q^{94} +5.03235 q^{95} +(0.979105 - 1.40176i) q^{96} +4.26779 q^{97} +(-1.23674 + 0.685911i) q^{98} +6.14320i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q + 2 q^{2} - 2 q^{4} - 6 q^{6} - 34 q^{7} + 8 q^{8} - 26 q^{9} - 4 q^{12} - 2 q^{14} - 8 q^{15} - 6 q^{16} - 20 q^{17} + 14 q^{18} - 4 q^{20} - 10 q^{22} - 20 q^{23} + 10 q^{24} - 22 q^{25} + 2 q^{28}+ \cdots + 2 q^{98}+O(q^{100}) \) 34 * q + 2 * q^2 - 2 * q^4 - 6 * q^6 - 34 * q^7 + 8 * q^8 - 26 * q^9 - 4 * q^12 - 2 * q^14 - 8 * q^15 - 6 * q^16 - 20 * q^17 + 14 * q^18 - 4 * q^20 - 10 * q^22 - 20 * q^23 + 10 * q^24 - 22 * q^25 + 2 * q^28 - 60 * q^30 + 16 * q^31 + 12 * q^32 - 8 * q^33 + 28 * q^34 - 4 * q^36 - 28 * q^38 + 8 * q^39 + 64 * q^40 + 8 * q^41 + 6 * q^42 + 24 * q^44 + 16 * q^46 + 24 * q^48 + 34 * q^49 + 10 * q^50 - 4 * q^52 - 18 * q^54 - 32 * q^55 - 8 * q^56 + 8 * q^57 + 44 * q^58 - 24 * q^60 + 60 * q^62 + 26 * q^63 - 2 * q^64 - 20 * q^65 + 24 * q^66 + 12 * q^68 + 64 * q^71 - 92 * q^72 - 22 * q^74 + 4 * q^76 + 20 * q^79 - 56 * q^80 - 6 * q^81 - 20 * q^82 + 4 * q^84 - 12 * q^86 - 56 * q^87 - 34 * q^88 - 4 * q^90 - 54 * q^92 + 12 * q^94 + 42 * q^96 + 2 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more